How to fade one material into the other?
A mesh face cannot be assigned to several materials. So you'll need to "incorporate" one of the material nodes into the other.

For convenience I have set face nodes/shader and lip nodes/shader each in a dedicated nodes group. That allows to use them both in your face or lips original materials. Doing so, imagine that 'as if' these nodes groups were replacing your initial materials.

Now select you lips faces and one ring more around. And assign these faces to a new UV map (called 'LipsIntensity' in the screen capture (1)).

Create a blank image (2).

Put your original face and mouth nodes respectively in a node group (select and group all the nodes except the output for each). So that you can reuse them (mainly the face shader) in the lips material (3 and arrows).
Now mix them so that the mix (4) factor is driven by the texture you added and itself based on the 'LipsIntensity' UV map (5).

Now go in the 3D view (6) and in texture paint mode and rendered mode. Make sure that your are painting on the 'LipsIntensity' texture (look at 'Available paint slots' in the 'Slot' panel of the texture paint mode).

Now simply paint in black over the lips, with a relatively large brush in order to obtain the ease you want (7 / 8).